Higher November 2019 Paper 2 Q17
17. The diagram shows a circle with centre \(O\).
Points \(A\), \(B\), \(C\) and \(D\) all lie on the circumference of the circle.
Diagram not drawn to scale
The radius of the circle is 3·6 cm, \(BC = 4{\cdot}1\) cm and \(B\hat{C}D = 93^\circ\).
Prove that \(D\hat{B}C = 52{\cdot}3^\circ\), correct to 3 significant figures.
You must show all your working and give a reason for each stage of your proof. [4]
| Scheme | Marks | Comments |
|---|---|---|
| \(\sin B\hat{A}C = \dfrac{4.1}{2 \times 3.6}\) | M1 | |
| \(180 - 93 - \sin^{-1} 4.1/7.2\) or \(180 - 93 - 34.7(\ldots)\) or equivalent | m1 | |
| Convincing 52.3(°) | A1 | |
| States: Angle in a semi-circle AND angles in the same segment | E1 | If no marks award SC1 for sight of \((\sin^{-1} 4.1/7.2 =)\) 34.7(....) |
| (4) |
Notes
Alternatives:
- using angles from the same chord and cos
- finding BAC, then CAD = 87 – BAC (cyclic quadrilateral), DBC = CAD (angles on the same arc)